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Why a QCW arc bends: the community's open question

Nobody knows. The straightness of a QCW arc depends on the room more than on the coil, and not one of the factors has ever been isolated.

CommonGnd4 August 202620 min read

Nobody knows. That is the honest headline, and it is worth saying at the top, because the straightness of a QCW's sword depends on the room more than it depends on the coil, and two people with the same machine get different results and go looking for a fault that is not there.

This is a collection of what has been observed and of the guesses attached to it. Where the data stops and the speculation starts is marked.

Two defects, constantly confused

Branching is the arc growing in all directions at once. Wander is the arc curving as a whole, sometimes right round into a loop.

They respond to frequency in opposite directions. Raise the frequency and branching gets better, because the channel runs hotter. Raise it and wander gets worse: a ramped VTTC at 2 MHz makes loops tens of centimetres across.

And there is a third, which is the one the experimenter names. davekni maps the two ways of making an arc longer onto two different failures at two different ends of it:

If length is added by increasing growth rate, branching is likely near tip. If length is added by increasing ramp time, electrostatic repulsion of the arc with itself near the base makes the path unstable, leading to branching near the base. This instability is obvious in my low frequency (100kHz) QCW experiments, but still visible in many QCW arcs towards end of ramp time (HVF 3140).

Read the last clause twice. Self-repulsion is not a curiosity of one 100 kHz experiment, it is what he says shows up late in the ramp on ordinary machines, which is exactly where a QCW spends its length.

So the band is a trade after all, and not the one this page used to name. It is length against stability, and the far end has a number attached: asked about swords above 500 kHz, davekni's answer is that staccato VTTCs make them at 1 to 2 MHz and that they are "Shorter arcs than most silicon or SiC ramped or QCW coils". High frequency buys a straight arc and spends length on it. Low frequency buys length and spends it on self-repulsion. The middle is where both are affordable, which is a better account of 200 to 500 kHz than the branching story below, and it is made of two sourced observations rather than one description of ours.

What people have seen

CJ has the most detailed set, on HVF 2434. Moved the machine to a different spot and the arc bent. Put it near a wooden cabinet, a wardrobe in his own words, and it straightened. He files that under "the arrangement of surrounding conductive materials such as wardrobes, tables, beds, and walls" and then says in the next breath that the wardrobe "is made of wood and does not conduct electricity", so the contradiction is his own and it is worth keeping: whatever the wardrobe did, he did not think it did it by conducting.

davekni answers that in the same thread and it is the only physics anybody offers for a cupboard: "though wood is not very conductive at low frequency, it can be significantly conductive at 12MHz. And dielectric materials should have some effect even if not conductive at all". Note the frequency he reaches for is 12 MHz, two orders above where these coils run, so the conductive half of that is doing less work here than it looks; the dielectric half needs no conductivity at all and is the part that survives. Cold winter, bending

down towards the ground; lit the stove, it warmed up, it straightened. Close to an iron frame, straighter, though he says that one was a small coil of his and not the machine the rest of the list came off (reply 9). The thickness of the grading ring barely mattered (reply 8).

And the plainest observation in any of the threads is davekni's, because it makes curvature a function of length rather than of the room: "even the curved arcs are comparatively straight if aborted earlier" (HVF 2397). Same coil, same room, same air; stop the ramp sooner and the arc is straighter. Whatever bends it needs length to do it in.

Jan, after maybe fifteen years of building coils, met this for the first time: arcs looping downward with a diameter under a metre, sometimes in an S. Dry air correlated with straighter arcs, though he calls the correlation weak and says outright that he does not really know. Temperature by itself did almost nothing. Opening the garage door to about ten degrees of outside air reduced the looping (HVF 1073).

Four hypotheses, none of them settled

The arc follows the toroid's field lines. Uspring's. A QCW arc is slow enough to follow the field. A small toroid holds little charge, so its influence falls away quickly with length, and the arc leaves for the nearest ground: floor, wall, ceiling. Outdoors there is no ceiling, so the loop goes to the ground or a wall.

A fifth hypothesis lives in the same thread and is not in the list above, because it is nobody's conclusion yet: that what matters is not the toroid's size but its thinness. It is Mads Barnkob's, not davekni's: the ring is "very wide and very thin" and "simply not powerful enough to keep the arcs from going back towards itself", and later that what is wanted is a large minor diameter. davekni owns only the test, and he is sceptical of the hypothesis he is proposing to test. The test is still the best controlled thing on this page, because it holds the frequency instead of the capacitance: a thicker top load, slightly smaller in diameter to keep the frequency where it was. Two things ride along with it. CJ has already run the cheap version and got nothing: thin grading rings swapped for thicker ones on small linear-arc coils, "The difference is not significant". And the thread contains a straightforward misreading, worth flagging because it is the kind that survives into summaries: Uspring writes "Perhaps Mads is right, that the top loads field doesn't matter much", and davekni corrects him, "I thought Mads was saying top load field does matter and that mine was not good". davekni has it right.

First, the arc does go away from the topload, which is the objection to answer. Somebody asks it that way in the same thread: the topload's field is strong enough to steer the arc, so should it not push the arc away rather than draw it back? Uspring's account agrees for the early arc. The field at the tip comes from the space charge just behind it and from the toroid, and initially that makes "the arc to grow straight and away from the top load". What changes is not the sign of that field but its weight: "the toroid doesn't hold much charge, so that its influence on the arc direction diminishes fast as the arc lengthens", said of a coil whose toroid is small against the arc it throws. So the loop is not the topload winning, it is the topload dropping out of the argument and something else taking over, and that something is next.

The arc as a distributed RC. The label is Jan's, and he raised it as an objection: he had always thought of the arc as a distributed RC network, which possibly cannot produce such large phase shifts. Uspring's own picture was a chain of resistances and space charges, and he accepted the RC framing in answering: the phase shift of a distributed RC network can be arbitrarily large, but it comes with an attenuation of voltage. He marks the whole idea as speculation. The mechanism is that a phase shift builds between the charge on the toroid and the charge at the tip, and as it approaches 180 degrees the tip is attracted back towards the toroid, giving a loop.

That attenuation can be put in numbers, and it is not a detail. On a distributed RC line γ = √(jωRC), so the loss and the phase per unit length are equal, α = β = √(ωRC/2). Reaching 180 degrees therefore costs exactly e^-π, which is 4.3 per cent of the toroid's voltage left at the tip, a factor of 23 down [derived]. That is Uspring's own doubt turned into a figure: the loop should form precisely when the arc has nothing left to grow with.

A spiral is a different claim and it comes with a test. Uspring separates a meandering arc from a spiralling one and gives the second a cause and a prediction: "Spiraling could be explained by the secondaries magnetic field. It should then always have the same helicity for every arc and it should be opposite to that of the secondary winding." That is falsifiable by looking, with no instrument: photograph enough arcs and either every spiral turns the same way against the winding or the explanation is wrong. Nobody in this corpus reports having checked, and it is the cheapest open question on this page.

And the frequency dependence is a square root, which two of Jan's numbers can be checked against. Phase per unit length goes as √f, so the length to 180 degrees goes as 1/√f. From his coil's ramp, 400 down to 350 kHz, to the VTTC's 2 MHz is a factor of √(2000/375) = 2.3, so a 1 m loop there predicts 43 cm at 2 MHz [derived, from the RC line and those two figures]. What was reported at 2 MHz is a few tens of centimetres. Read that 1 m as a diameter, which is Jan's own word for it above. This note used to add that the check "only works with the diameter", which read as though the interpretation had been chosen to make the sum come out. It had not, and the requirement is duller: the scaling is a ratio, so it holds whichever quantity you use as long as it is the same one at both ends. Taking Jan's metre as a radius and comparing the answer against a diameter reported at 2 MHz mixes the two, and that is why it misses by a factor of two. The model predicts a length along the channel, and what gets reported is a width across the room, so one line of geometry connects them. A channel that has turned through 180 degrees at even curvature is a semicircle: its length is L = πr, so the loop's diameter is 2L/π, about 0.64 L [derived]. A loop a metre across is therefore an arc about 1.57 m long, and that is the figure to compare against a coil's reach, not the metre. Nobody has published both numbers for one arc, which is the cheapest way this model could be falsified and has not been tried.

Nobody has a mechanism for the air at all, and the man with the models says so. Asked to explain Jan's photograph, Uspring answers "I can't", and then: "And I also don't have the slightest idea how air temperature or humidity could cause arcs to bend or not. Does anybody have a suggestion?" One suggestion came back in the next post and it is still the only one on the record: that humidity changes how fast the channel cools, or costs it energy evaporating water vapour on the way through. Nobody has tested either.

Uniformity rather than absolute values. davekni has no conclusion; his best guess is that what matters is how uniform the temperature and humidity are rather than what they are, with the arc bending towards pockets of warmer air where the breakdown voltage is slightly lower. That last part is testable, which "uniformity matters" on its own is not. He also notes that dielectrics matter and that wood, which is not very conductive at low frequency, can be significantly conductive at 12 MHz, which fits CJ's wooden cabinet. Read the 12 rather than "at radio frequencies": it is thirty times a QCW's own operating frequency, so it is a statement about the material's trend and not about what the cabinet is doing at 400 kHz.

Humidity. Mads: a warm room means lower relative humidity, so drier air, so the arc's attachment to ground behaves differently (HVF 2434).

What the data does not support

There is no single factor, and the temperature line is worse than inconsistent. This page used to say that temperature "worked for CJ and did almost nothing for Jan", which is too kind to it. Jan's result is not null, it is opposite in sign:

CJ    cold winter, arc bending down
      lit the stove, the room warmed, it straightened   heating helped

Jan   heating the air to room temperature
      "didn't help much"                                heating did not help
      opening the garage door and letting outside
      air in: "the looping decreased a lot"             fresh air helped

Both men heated the room, and it worked for one of them. That is the sharp form of it, and it is sharper than saying temperature was inconsistent.

Read Jan's second line carefully, because it is not the temperature claim it looks like. His words are "Even though it was relatively cold (~10 degrees C), the looping decreased a lot", which puts the cold down as something the result happened in spite of. His variable was the air itself, exchanged with outdoors, and he says so. So there is no builder on this page claiming that colder is straighter; there is one claiming heating helped and one claiming heating did not while fresh air did.

The one pressure observation has no located source and nobody has repeated it.

The two results do line up, but only through a quantity neither of them measured. Heating a room without adding water lowers its relative humidity, so CJ's stove made the air drier. Outside air at ten degrees brought into a warmer garage warms up on the way in, and its relative humidity falls as it does, so Jan's open door made the air drier as well. Both point the same way once the axis is relative humidity instead of temperature, and that direction is the one Jan himself reports, dry air with straighter arcs. Which is a hypothesis and not a finding, and it should be read knowing what it rests on: a correlation its own author calls weak and says outright he does not really know, plus an assumption about the absolute humidity of outdoor air in Jan's garage that nobody took a reading of. It earns its place by being the only account that fits both results rather than discarding one, and it is falsifiable by the cheapest instrument in this whole piece.

Almost none of this is a direct experiment. It is nearly all "I changed the surroundings and it behaved differently", where several things changed at once.

What to do with it anyway

If your arc bent after a move or a cold snap, look at the room before you touch the tuning. That is the most useful thing in this whole piece.
Do not compare your results to somebody's video without knowing the conditions it was shot in.
If it loops down towards the base, a bigger toroid is hypothesis one. Try it knowing that the largest top load on the forum produces mostly curved arcs, so the evidence there is against rather than absent.
Check whether it is actually branching rather than wandering. Branching has its own causes: the lower pole, too fast a ramp, a corner in the ramp, or residual voltage left on the bus.

What would close it

One factor isolated. One coil, one room, change only the humidity, or only the pressure, film it on one camera.
The thickness test rather than the toroid test. Two top loads of different thickness at the same frequency beats two of different capacitance, because the second changes the tuning along with the geometry.
The frequency dependence on one machine, rather than by comparing different ones. The square root above says what to expect from it.
Move the breakout point rather than the top load. Uspring's own suggestion to davekni, and it is better controlled than any toroid swap because it changes the field's geometry while leaving the tuning alone: a breakout rod of a metre, or one set off centre, or one at an angle. His reason it is safe to try is that "Adding extra capacitance to the top likely won't affect tuning very much, since the coupling is so large". It also tests the field-line hypothesis directly, since that hypothesis says the direction the breakout faces is what picks which surface the field lines end on. Not run.
A hygrometer, which is the cheapest thing on this list. Every room result on this page is a temperature story told by people who were not measuring humidity, and the two temperature results point opposite ways while their humidity readings, if anybody had taken them, would point the same way. Log relative humidity beside each run and the leading hypothesis on this page either survives its first real test or dies.
Numbers. Every observation above is qualitative, and that is still the gap. The two figures on this page, the 4.3 per cent and the 43 cm, are consequences of a model rather than measurements, and the second is the model's only successful prediction so far.

Whoever collects even one of those measurements closes a question the community has not managed to close.

The QCW department diagram draws its arc straight, which is the good case rather than the ordinary one. The records page collects the builds that got there.

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